578 Words3 Pages

Revision Year 12 Maths B, Term 4
1. The function, y=3cosx+5 has an amplitude of 3 and a mean value of 5.
Using these values, the range can be found to be 2≤y≤8 .
Find the range of the function y=4cosx+7
2. Find the exact value of tan600 (Hint, draw a standard triangle to help)
3. The -coordinate of the stationary point of a function can be found by following these steps: * differentiate the function * let the derivative = 0 * solve for
Find the -coordinate of the stationary point of the function,
4. Fully simplify: 3sin2θ+5cos2θ
5. A copper mine produces t tonnes of copper each week at a total cost of $C given by:
Ct=1000 -70t+5t2 .
How many tonnes of copper are needed to be*…show more content…*

Using algebraic methods, find the value for x which will give the greatest area. 2 In a West Queensland town on a day in the middle of winter, the temperature (T) in degrees Celsius is modelled by the function: T=16-8cosπx12, where x is the number of hours since 6 am. Lynne refuses to leave her nice warm house until the temperature has risen to 12º C. What is the earliest time she can leave? 3. Fully simplify the expression, tanx1+ tan2x . Use the knowledge that sin x= -35 and π2≤x ≤ 3π2 to express your simplified expression as an exact answer in fraction form. 4 Heat loss from electric hot water systems is an environmental issue. It is recognised that the heat loss from a closed, full hot water tank is proportional to the surface area of the tank. Determine the ratio of the heat loss from a 1m3 cylindrical tank of optimum dimensions (that is, the dimensions of the cylindrical tank for which the heat loss is a minimum) to the heat loss from a cubic tank with the same volume. Which tank design do you recommend as being more “environmentally friendly”? Remember: Vcylinder= πr2h SA cylinder= 2πr2+

Using algebraic methods, find the value for x which will give the greatest area. 2 In a West Queensland town on a day in the middle of winter, the temperature (T) in degrees Celsius is modelled by the function: T=16-8cosπx12, where x is the number of hours since 6 am. Lynne refuses to leave her nice warm house until the temperature has risen to 12º C. What is the earliest time she can leave? 3. Fully simplify the expression, tanx1+ tan2x . Use the knowledge that sin x= -35 and π2≤x ≤ 3π2 to express your simplified expression as an exact answer in fraction form. 4 Heat loss from electric hot water systems is an environmental issue. It is recognised that the heat loss from a closed, full hot water tank is proportional to the surface area of the tank. Determine the ratio of the heat loss from a 1m3 cylindrical tank of optimum dimensions (that is, the dimensions of the cylindrical tank for which the heat loss is a minimum) to the heat loss from a cubic tank with the same volume. Which tank design do you recommend as being more “environmentally friendly”? Remember: Vcylinder= πr2h SA cylinder= 2πr2+

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